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UKMT Junior Mathematical Challenge, 2016

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Beatrix places dominoes on a $5\times 5$ board, either horizontally or vertically, so that each domino covers two small squares. She stops when she cannot place another domino, as in the example shown in the diagram. When Beatrix stops, what is the largest possible number of squares that may still be uncovered?

(A) $4$ (B) $5$ (C) $6$ (D) $7$ (E) $8$

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